Publications and Preprints

  • A Note on Optimization Formulations of Markov Decision Processes. [pdf]

Lexing Ying and Yuhua Zhu.

Communications in Mathematical Sciences, 2021, to appear.

  • The Vlasov Fokker Planck Equation with High Dimensional Parametric Forcing Term. [pdf]

Shi Jin, Yuhua Zhu*, and Enrique Zuazua. 

Numerische Mathematik, 2021.

  • Borrowing From the Future: Addressing Double Sampling in Model-free Control. [pdf]

Yuhua Zhu, Zachary Izzo and Lexing Ying

Mathematical and Scientific Machine Learning, PMLR, 2021.

  • Why resampling outperforms reweighting for correcting sampling bias with stochastic gradients. [pdf]

Jing An, Lexing Ying, Yuhua Zhu*.

International Conference on Learning Representations (ICLR), 2021.

  • A Sharp Convergence Rate for a Model Equation of the Asynchronous Stochastic Gradient Descent. [pdf]

Yuhua Zhu, Lexing Ying.​ 

Communications in Mathematical Sciences, 19(3), 851-863, 2020.

  • Borrowing From the Future: An Attempt to Address Double Sampling. [pdf]

Yuhua Zhu and Lexing Ying.

Mathematical and Scientific Machine Learning, PMLR 107:246-268, 2020. 

  • On large batch training and sharp minima: A Fokker-Planck perspective. [pdf]

Xiaowu Dai and Yuhua Zhu*.

Journal of Statistical Theory and Practice (JSTP), special issue on "Advances in Deep Learning", 2020. 

  • A consensus-based global optimization method for high dimensional machine learning problems. [pdf]

Jose Carrillo, Shi Jin, Lei Li and Yuhua Zhu*

ESAIM: Control, Optimisation and Calculus of Variations 27, S5, 2020.

  • A Local Sensitivity and Regularity Analysis for the Vlasov-Poisson-Fokker-Planck System with Multi-dimensional Uncertainty and the Spectral Convergence of the Stochastic Galerkin Method. [pdf]

Yuhua Zhu. 

Networks and Heterogeneous Media, 14(4), 677-707, 2019.

  • An Uncertainty Quantification Approach to the Study of Gene Expression Robustness. [pdf]

Pierre Degond, Shi Jin and Yuhua Zhu*.

Methods and Applications of Analysis (A special issue in honor of the 80th birthday of Prof. Ling Hsiao), 2019.

  • Hypocoercivity and Uniform Regularity for the Vlasov-Poisson-Fokker-Planck System with Uncertainty and Multiple Scales. [pdf]

Shi Jin and Yuhua Zhu*. 

SIAM Journal on Mathematical Analysis, 50, 1790-1816, 2018.

  • The Vlasov-Poisson-Fokker-Planck System with Uncertainty and a One-Dimensional Asymptotic-Preserving Method. [pdf]

Yuhua Zhu and Shi Jin.

Multiscale Modeling and Simulation, 15, 1502-1529, 2018.

  • Operator Augmentation for Model-based Policy Evaluation. [pdf]

Xun Tang, Lexing Ying and Yuhua Zhu*. 


  • Variational Actor-Critic Algorithms. [pdf]

Yuhua Zhu and Lexing Ying.


  • Stabilization of the Vlasov Fokker Planck Equation with Reflective Boundary Condition. [pdf]

Michael Herty, Shi Jin and Yuhua Zhu*.


Ph.D. Thesis

  • Uncertainty Quantification for Fokker Planck Type Equations and Related Problems in Machine Learning. [pdf]

Yuhua Zhu.

Ph.D. Thesis,  Department of Mathematics, UW-Madison, 2019.